Lithographic apparatus and device manufacturing method

ABSTRACT

A lithographic apparatus includes a support structure configured to hold a patterning device, the patterning device configured to pattern a beam of radiation according to a desired pattern, a substrate table configured to hold a substrate and a projection system configured to project the beam as patterned onto a target portion of the substrate. The lithographic apparatus further includes a polarization modifier disposed in a path of the beam. The polarization modifier comprises a material having a radially varying birefringence.

BACKGROUND

1. Field

The present invention relates to a lithographic apparatus and a methodof making a device.

2. Background

A lithographic apparatus is a machine that applies a desired patternonto a target portion of a substrate. Lithographic apparatus can beused, for example, in the manufacture of integrated circuits (ICs). Inthat circumstance, a patterning device, which is alternatively referredto as a mask or a reticle, may be used to generate a circuit patterncorresponding to an individual layer of the IC, and this pattern can beimaged onto a target portion (e.g. comprising part of, one or severaldies) on a substrate (e.g. a silicon wafer) that has a layer ofradiation-sensitive material (resist). In general, a single substratewill contain a network of adjacent target portions that are successivelyexposed. Known lithographic apparatus include so-called steppers, inwhich each target portion is irradiated by exposing an entire patternonto the target portion at one time, and so-called scanners, in whicheach target portion is irradiated by scanning the pattern through theprojection beam in a given direction (the “scanning”-direction) whilesynchronously scanning the substrate parallel or anti-parallel to thisdirection.

Development of new apparatus and methods in lithography have led toimprovements in resolution of the imaged features, such as lines andcontact holes or vias, patterned on a substrate, possibly leading to aresolution of less than 50 nm. This may be accomplished, for example,using relatively high numerical aperture (NA) projection systems(greater than 0.75 NA), a wavelength of 193 nm or less, and a plethoraof techniques such as phase shift masks, non-conventional illuminationand advanced photoresist processes.

However, certain small features such as contact holes are especiallydifficult to fabricate. The success of manufacturing processes atsub-wavelength resolutions will rely on the ability to print lowmodulation images or the ability to increase the image modulation to alevel that will give acceptable lithographic yield.

Typically, the industry has used the Rayleigh criterion to evaluate thecritical dimension (CD) and depth of focus (DOF) capability of aprocess. The CD and DOF measures can be given by the followingequations:CD=k ₁(λ/NA),andDOF=k ₂(λ/NA ²),where λ is the wavelength of the illumination radiation, k₁ and k₂ areconstants for a specific lithographic process, and NA is the numericalaperture.

Additional measures that provide insight into the difficultiesassociated with lithography at the resolution limit include the ExposureLatitude (EL), the Dense:Isolated Bias (DIB), and the Mask ErrorEnhancement Factor (MEEF). The exposure latitude describes thepercentage dose range where the printed pattern's critical dimension(CD)is within acceptable limits. For example, the exposure latitude maybe defined as the change in exposure dose that causes a 10% change inprinted line width. Exposure Latitude is a measure of reliability inprinting features in lithography. It is used along with the DOF todetermine the process window, i.e., the regions of focus and exposurethat keep the final resist profile within prescribed specifications.Dense:Isolated Bias is a measure of the size difference between similarfeatures, depending on the pattern density. Finally, the MEEF describeshow patterning device CD errors are transmitted into substrate CDerrors.

Among the trends in lithography is to reduce the CD by lowering thewavelength used, increasing the numerical aperture, and/or reducing thevalue of k1. However, increasing the numerical aperture would also leadto a decrease in the DOF which ultimately could lead to limitations inprocess latitude. This can also be understood by combining the above twoequations to obtain:DOF=(k ₂ /k ₁ ²)(CD ²/λ).

From this equation it can be seen that a decrease in CD, i.e., anincrease in resolution, would lead to a decrease in DOF which isunwanted in most lithographic processes and specifically in the processof printing contact holes.

SUMMARY

According to an aspect of the present invention, there is provided alithographic apparatus including a support structure configured to holda patterning device, the patterning device configured to pattern a beamof radiation according to a desired pattern, a substrate tableconfigured to hold a substrate and a projection system configured toproject the patterned beam onto a target portion of the substrate. Thelithographic apparatus further includes a polarization modifier disposedin a path of the beam of radiation. The polarization modifier comprisesa material having a radially varying birefringence.

According to another aspect of the present invention, there is provideda lithographic apparatus including a support structure configured tohold a patterning device, the patterning device configured to pattern abeam of radiation according to a desired pattern, a substrate tableconfigured to hold a substrate and a projection system configured toproject the patterned beam onto a target portion of the substrate. Thelithographic apparatus further includes a polarization modifier disposedin a path of the beam of radiation. The polarization modifier comprisesa material having a radially continuously varying birefringence.

According to yet another aspect of the present invention there isprovided a method for manufacturing a device. The method includesprojecting a patterned beam of radiation through a polarization modifiercomprising a material having a radially varying birefringence onto atarget portion of a substrate.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin-film magnetic heads, etc. Theskilled artisan will appreciate that, in the context of such alternativeapplications, any use of the terms “wafer” or “die” herein may beconsidered as synonymous with the more general terms “substrate” or“target portion”, respectively. The substrate referred to herein may beprocessed, before or after exposure, in for example a track (a tool thattypically applies a layer of resist to a substrate and develops theexposed resist) or a metrology or inspection tool. Where applicable, thedisclosure herein may be applied to such and other substrate processingtools. Further, the substrate may be processed more than once, forexample in order to create a multi-layer IC, so that the term substrateused herein may also refer to a substrate that already contains multipleprocessed layers.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of 365, 248, 193, 157 or 126 nm) and extremeultra-violet (EUV) radiation (e.g. having a wavelength in the range of5-20 nm), as well as particle beams, such as ion beams or electronbeams.

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a beam with apattern in its cross-section such as to create a pattern in a targetportion of the substrate. It should be noted that the pattern impartedto the beam may not exactly correspond to the desired pattern in thetarget portion of the substrate. Generally, the pattern imparted to thebeam will correspond to a particular functional layer in a device beingcreated in the target portion, such as an integrated circuit.

A patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions; in this manner, thereflected beam is patterned.

The support structure holds the patterning device in a way depending onthe orientation of the patterning device, the design of the lithographicapparatus, and other conditions, such as for example whether or not thepatterning device is held in a vacuum environment. The support can usemechanical clamping, vacuum, or other clamping techniques, for exampleelectrostatic clamping under vacuum conditions. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired and which may ensure that the patterning device is at a desiredposition, for example with respect to the projection system. Any use ofthe terms “reticle” or “mask” herein may be considered synonymous withthe more general term “patterning device”.

The term “projection system” used herein should be broadly interpretedas encompassing various types of projection system, including refractiveoptical systems, reflective optical systems, and catadioptric opticalsystems, as appropriate for example for the exposure radiation beingused, or for other factors such as the use of an immersion fluid or theuse of a vacuum. Any use of the term “projection lens” herein may beconsidered as synonymous with the more general term “projection system”.

The illumination system may also encompass various types of opticalcomponents, including refractive, reflective, and catadioptric opticalcomponents for directing, shaping, or controlling the beam of radiation,and such components may be referred to below, collectively orsingularly, as a “lens”.

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more support structures). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein a surface ofthe substrate is immersed in a liquid having a relatively highrefractive index, e.g. water, so as to fill a space between a finalelement of the projection system and the substrate. Immersion liquidsmay also be applied to other spaces in the lithographic apparatus, forexample, between the patterning device and a first element of theprojection system. Immersion techniques are well known in the art forincreasing the numerical aperture of projection systems.

The methods described herein may be implemented as software, hardware ora combination. In an embodiment, there is provided a computer programcomprising program code that, when executed on a computer system,instructs the computer system to perform any or all of the methodsdescribed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will become more apparent andmore readily appreciated from the following detailed description of thepresent exemplary embodiments of the invention, taken in conjunctionwith the accompanying drawings, of which:

FIG. 1 schematically depicts a lithographic projection apparatusaccording to an embodiment of the invention;

FIG. 2 depicts a geometry for focus computation used in calculating adepth of focus according to an embodiment of the invention;

FIGS. 3A and 3B show intensity profiles of a projection beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for a dry projection system;

FIGS. 4A and 4B show intensity profiles of a projection beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for an immersion projection system;

FIG. 5 depicts a polarization modifier having a radially increasinglinear birefringence according to an embodiment of the invention;

FIGS. 6A and 6B show intensity profiles of a projection beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for a dry projection system using the polarization modifier ofFIG. 5 in accordance with an embodiment of the invention;

FIGS. 7A and 7B show intensity profiles of a projection beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for an immersion projection system using the polarizationmodifier of FIG. 5 in accordance with an embodiment of the invention;

FIGS. 8A and 8B show intensity profiles of a projection beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for a dry projection system using a polarization modifierhaving circular birefringence in accordance with an embodiment of theinvention;

FIGS. 9A and 9B show intensity profiles of an illumination beam atdifferent focus points obtained, respectively, in the XZ plane and theYZ plane, for an immersion projection system using a polarizationmodifier having circular birefringence in accordance with an embodimentof the invention;

FIGS. 10A and 10B show an intensity contour map, respectively, in the Xzplane and the YZ plane, for various configurations including a systemwithout birefringence, a system with a polarization modifier havinglinear birefringence and a system with a polarization modifier havingcircular birefringence;

FIGS. 11A, 11B and 11C show plots of Bossung curves for a dry projectionsystem in the XZ plane, for a system without birefringence, a systemwith a polarization modifier having linear birefringence and a systemwith a polarization modifier having circular birefringence,respectively;

FIGS. 12A, 12B and 12C show plots of Bossung curves for a dry projectionsystem in the YZ plane, for a system without birefringence, a systemwith a polarization modifier having linear birefringence and a systemwith a polarization modifier having circular birefringence,respectively;

FIG. 13 is a schematic representation of a space variant optical elementthat can be used for varying circular birefringence in the pupil planeof the projection system according to an embodiment of the invention;

FIG. 14 is a schematic representation of a rotator that can be used forvarying circular birefringence in the pupil plane of the projectionsystem according to an embodiment of the invention; and

FIG. 15 schematically depicts a lithographic projection apparatusutilizing a polarization modifier according to an embodiment of theinvention.

DETAILED DESCRIPTION

FIG. 1 schematically depicts a lithographic apparatus according to aparticular embodiment of the invention. The apparatus comprises:

-   an illumination system (illuminator) IL adapted to condition a beam    PB of radiation (e.g. UV radiation).-   a support structure (e.g. a mask table) MT configured to hold a    patterning device (e.g. a mask) MA and connected to first    positioning device PM configured to accurately position the    patterning device with respect to item PL;-   a substrate table (e.g. a wafer table) WT configured to hold a    substrate (e.g. a resist-coated wafer) W and connected to second    positioning device PW configured to accurately position the    substrate with respect to item PL; and-   a projection system (e.g. a refractive projection lens) PL adapted    to image a pattern imparted to the beam PB by the patterning device    MA onto a target portion C (e.g. comprising one or more dies) of the    substrate W.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above).

The illuminator IL receives a beam of radiation from a radiation sourceSO. The source and the lithographic apparatus may be separate entities,for example when the source is an excimer laser. In such cases, thesource is not considered to form part of the lithographic apparatus andthe radiation beam is passed from the source SO to the illuminator ILwith the aid of a beam delivery system BD comprising for examplesuitable directing mirrors and/or a beam expander. In other cases thesource may be integral part of the apparatus, for example when thesource is a mercury lamp. The source SO and the illuminator IL, togetherwith the beam delivery system BD if required, may be referred to as aradiation system.

The illuminator IL may comprise an adjusting device AM for adjusting theangular intensity distribution of the beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator ILgenerally comprises various other components, such as an integrator INand a condenser CO. The illuminator provides a conditioned beam ofradiation, referred to as the projection beam PB, having a desireduniformity and intensity distribution in its cross-section.

The projection beam PB is incident on the patterning device MA, which isheld on the support structure MT. Having traversed the patterning deviceMA, the projection beam PB passes through the projection system PL,which focuses the beam onto a target portion C of the substrate W. Withthe aid of the second positioning device PW and position sensor IF (e.g.an interferometric device), the substrate table WT can be movedaccurately, e.g. so as to position different target portions C in thepath of the beam PB. Similarly, the first positioning device PM andanother position sensor (which is not explicitly depicted in FIG. 1) canbe used to accurately position the patterning device MA with respect tothe path of the beam PB, e.g. after mechanical retrieval from a masklibrary, or during a scan. In general, movement of the support structureMT and the substrate table WT will be realized with the aid of along-stroke module (coarse positioning) and a short-stroke module (finepositioning), which form part of the one or both of the positioningdevices PM and PW. However, in the case of a stepper (as opposed to ascanner) the support structure MT may be connected to a short strokeactuator only, or may be fixed. Patterning device MA and substrate W maybe aligned using patterning device alignment marks M1, M2 and substratealignment marks P1, P2. The depicted apparatus can be used in thefollowing preferred modes:

-   -   1. In step mode, the support structure MT and the substrate        table WT are kept essentially stationary, while an entire        pattern imparted to the projection beam is projected onto a        target portion C at one time (i.e. a single static exposure).        The substrate table WT is then shifted in the X and/or Y        direction so that a different target portion C can be exposed.        In step mode, the maximum size of the exposure field limits the        size of the target portion C imaged in a single static exposure.    -   2. In scan mode, the support structure MT and the substrate        table WT are scanned synchronously while a pattern imparted to        the projection beam is projected onto a target portion C (i.e. a        single dynamic exposure). The velocity and direction of the        substrate table WT relative to the support structure MT is        determined by the (de-)magnification and image reversal        characteristics of the projection system PL. In scan mode, the        maximum size of the exposure field limits the width (in the        non-scanning direction) of the target portion in a single        dynamic exposure, whereas the length of the scanning motion        determines the height (in the scanning direction) of the target        portion.    -   3. In another mode, the support structure MT is kept essentially        stationary holding a programmable patterning device, and the        substrate table WT is moved or scanned while a pattern imparted        to the projection beam is projected onto a target portion C. In        this mode, generally a pulsed radiation source is employed and        the programmable patterning device is updated as required after        each movement of the substrate table WT or in between successive        radiation pulses during a scan. This mode of operation can be        readily applied to maskless lithography that utilizes a        programmable patterning device, such as a programmable mirror        array of a type as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

When a high numerical aperture is used for a projection system, forexample a numerical aperture of 0.93 for a dry projection system usingunpolarized illumination, to increase the resolution, this can lead to adepth of focus that is symmetrical but relatively small.

This is illustrated, for example, in FIGS. 3A and 3B which show theresults of a simulation of a three dimensional focus of a projectionsystem with a numerical aperture of 0.93 on a resist material having arefractive index of 1.8 and with a refractive index of the mediumbetween the projection system and the substrate equal to about 1 (i.e.,a dry projection system). In the simulation, a perfect projectionsystem, i.e., a projection system without aberrations, is assumed andall simulations are performed at a radiation wavelength of 193.36 nm.However, it should be appreciated that the above and other parametersherein are only one possible set of parameters and other possible setsof parameters are within the scope of the present invention. Forexample, the wavelength can be selected to be a different wavelengthvalue such as, for example, about 157 nm.

For purposes of the present description, it is assumed that thesubstrate with the resist layer is lying in the XY plane and theprojection beam propagates along the Z coordinate. FIG. 2 shows ageometry for focus computation in which the coordinates (p, q) representthe pupil coordinates, E is the electromagnetic field vector, k is thepropagation vector, θ is the angle representing the focus of a beam ofradiation by the projection system, represented schematically in FIG. 2by a lens at an exit pupil, φ is the azimuthal angle between the planeformed by the vectors E and k and the X coordinate and n is therefractive index of the medium through which the beam of radiationpasses to reach a surface of a substrate (in plane XY).

FIG. 3A shows an intensity profile of the projection beam at variousfocus points around the best focus in the XZ plane and FIG. 3B shows anintensity profile of the projection beam at various focus points aroundthe best focus in the YZ plane. The position of the focus points aremapped in three coordinates X, Y and Z with the Z coordinaterepresenting the range of focus (e.g., depth of focus), and theintensity at each focus point (X, Y, Z) is given by a shade of color orgray. The darkest shade of gray or color at the center of the intensityprofile corresponds to the maximum intensity (the intensity isapproximately 0.9). The color or gray scale on the right of FIG. 3A andFIG. 3B gives a measure of the intensity.

In the results of the simulation shown in FIGS. 3A and 3B, the depth offocus, which is the total range of focus that can be tolerated, that is,the range of focus that keeps the resulting printed feature within avariety of specifications (such as line width, sidewall angle, resistloss, and/or exposure latitude), is between about −200 and about 200 inthe Z coordinate with the best focus being at 0.

When the numerical aperture is increased to 1.2, for example bysimulating the use of water (with a refractive index of 1.44) as animmersion liquid between the projection system and the substrate, theintensity profiles obtained previously through the simulation arealtered as shown in FIGS. 4A and 4B.

FIG. 4A shows an intensity profile of the projection beam at variousfocus points around the best focus in the XZ plane and FIG. 4B shows anintensity profile of the projection beam at various focus points aroundthe best focus in the YZ plane. The position of the focus points aremapped in three coordinates X, Y and Z with the Z coordinaterepresenting the range of focus and the intensity at each focus point(X, Y, Z) is given by a shade of color or gray. The darkest shade ofgray or color at the center of the intensity profile represents themaximum intensity (the intensity is approximately 0.8). The color orgray scale on the right of FIG. 4A and FIG. 4B gives a measure of theintensity.

In the results of the simulation shown in FIGS. 4A and 4B, the depth offocus is between approximately −200 and approximately 200 in the Zcoordinate with the best focus being at 0. A small depth of focusreduces the process window for a given process. This problem may becomemore acute when the process includes imaging contact holes which are 3dimensional in nature as imaging of contact holes may require morecareful considerations in terms of process window.

To improve the depth of focus, it is proposed to use polarization toincrease the depth of focus. This is accomplished by displacing twoorthogonally polarized foci laterally with respect to each other. Thesuperposition of the two orthogonally displaced foci forms a combinedfocus with increased depth of focus.

In an embodiment of the invention, a polarization modifier with radiallyvarying (for example, increasing) linear birefringence, formed from alinearly birefringent material, is introduced into the imaging system toincrease the depth of focus. In an embodiment, such a polarizationmodifier is a retarder.

A linearly birefringent material, such as calcite (CaCO₃), will dividean entering beam of monochromatic radiation into two beams havingorthogonal polarizations. The beams will propagate in differentdirections and have different propagation speeds. Depending on whetherthe birefringent material is uniaxial or biaxial, there will be one ortwo directions within the material along which the beams will remainco-linear and continue to propagate with the same speed. Thesedirections are called the optic axes directions. For example, if thematerial is a plane-parallel plate, and the beam is not collinear withthe optic axes directions, the radiation will emerge as two separate,orthogonally polarized beams. The two beams within the birefringentcrystal are referred to as the ordinary ray and extraordinary ray,respectively. The polarization of the extraordinary ray lies in theplane containing the direction of propagation of the beam and the opticaxis, and the polarization of the ordinary ray is perpendicular to thisplane.

FIG. 5 shows a polarization modifier having radially increasing (forexample, quadratically increasing) linear birefringence. The color orgrayed scale on the right of FIG. 5 gives a measure of the magnitude ofbirefringence with the lowest value being 0 and the highest value being100. The magnitude of the birefringence as a function of the pupilcoordinates p and q is given by:${\Delta\quad n} = {\exp\left\{ {i\quad\Delta\quad\varphi_{0}\frac{p^{2} + q^{2}}{{NA}^{2}}} \right\}}$and the orientation α is given by: ${\tan\quad\alpha} = \frac{q}{p}$where n is the refractive index of the birefringent material of thepolarization modifier, Δn is the variation of the refractive index inthe (p, q) coordinates, i is the imaginary number, NA is the numericalaperture and Δφ₀ is the value of the retardance at the rim of theaperture.

The results of a simulation using the polarization modifier of FIG. 5are presented in FIGS. 6A and 6B for a projection system with anumerical aperture of 0.93 on a resist material having a refractiveindex of 1.8 and with a refractive index of the medium between theprojection system and the substrate equal to about 1 (i.e., a dryprojection system). In the simulation, a perfect projection system,i.e., a projection system without aberrations, is assumed and allsimulations are performed at a wavelength of 193.36 nm. FIG. 6A shows anintensity profile of the projection beam at various focus points aroundthe best focus in the XZ plane and FIG. 6B shows an intensity profile ofthe projection beam at various focus points around the best focus in theYZ plane. In FIG. 6A, it can be seen that the upper focus points (forexample, focus points around a Z of 200) are elongated in the Xdirection. On the other hand, it can be seen in FIG. 6B that the lowerfocus points (for example, focus points around a Z of −200) areelongated in the Y direction. This is because a linear polarized focusis asymmetrical along the direction of polarization and perpendicular tothe direction of polarization, i.e. the width of the focus is largeralong the direction of polarization than along a direction perpendicularto the direction of polarization. Therefore, the upper focus ispolarized along the X direction and the lower focus is polarized alongthe Y coordinate.

When the numerical aperture is increased to 1.2, for example bysimulating the use of water (with a refractive index of 1.44) as animmersion liquid between the projection system and the substrate, theintensity profiles obtained in the case of a dry projection system witha linear birefringent polarization modifier are modified as shown inFIGS. 7A and 7B. FIG. 7A shows an intensity profile of the projectionbeam at various focus points around the best focus in the XZ plane andFIG. 7B shows an intensity profile of the projection beam at variousfocus points around the best focus in the YZ plane. The asymmetricprofile of the intensity of the focus remains generally the same as theone obtained in the case of a dry projection system.

However, the depth of focus remains generally the same or slightlyincreased in the Z direction when comparing the results obtained withoutusing birefringence (FIGS. 3A and 3B) and the results obtained with theuse of a linear birefringent polarization modifier (FIGS. 6A and 6B) inthe case of a dry projection system. This trend can also be observed inthe case of an immersion projection system where the results obtainedwithout using birefringence (FIGS. 4A and 4B) and the results obtainedwith the use of a linear birefringent polarization modifier (FIGS. 7Aand 7B) show a depth of focus in the Z direction which remains generallyunchanged or slightly increased. Consequently, the use of a linearbirefringent polarization modifier does not substantially increase thedepth of focus but does enhance the width of focus in the X and Ydirections.

To improve depth of focus, a polarization modifier with circularbirefringence (for example, a pupil filter with circular birefringence)is introduced into the projection system instead of a polarizationmodifier with linear birefringence. This is motivated by the fact that,contrary to the non-symmetrical nature of a focus of a linearlypolarized wave, the focus of a circularly polarized wave is symmetrical.

Contrary to a material exhibiting a linear birefringence (such ascalcite) in which there exist a direction or directions where theordinary (O) and the extraordinary (E) ray are equal, in a materialexhibiting circular birefringence (such as quartz) there is no suchdirection(s). The direction of the optical axis for circularbirefringent crystals is the direction in which the difference in theindices for the O and E ray is a minimum. For example, if a quartz plateis cut such that its optic axis is normal to the surfaces of the plate,and a ray of linearly polarized light is incident parallel to the opticaxis, the ray will be separated into two collinear, circularly polarizedrays. The ordinary (O) and the extraordinary (E) rays will have oppositesenses of circular polarization and will travel at different speeds. Theplane of polarization rotates about the optic axis as the beampenetrates the plate. The amount of rotation is directly proportional tothe depth of penetration, and ultimately to the thickness of the plate.The superposition of two counter-rotating circular polarizationsproduces linear polarization without any intermediate ellipticalpolarization states. The polarization of the O and E rays in quartzrapidly changes from circular to elliptical even for directions whichdepart only slightly from the optical axis. For this reason, deviceswhich depend on circular polarization are typically effective only whenhighly collimated radiation propagates parallel to the optical axisdirection.

A polarization modifier with circular birefringence is an opticalelement that provides a retardance between left and right circularpolarized radiation. In an embodiment, such an optical element is arotator having the following Jones matrix: $J = \begin{pmatrix}{\cos\quad\beta} & {{- \sin}\quad\beta} \\{\sin\quad\beta} & {\cos\quad\beta}\end{pmatrix}$where the rotation angle β depends on the radial pupil coordinate (p,q), the numerical aperture NA, and the value of the rotation at the rimof the aperture β₀ according to the following equation:$\beta = {\beta_{0}\frac{p^{2} + q^{2}}{{NA}^{2}}}$

In an embodiment, a simulation is performed with a numerical aperture NAequal to 0.93 (for a dry projection system) and equal to 1.2 (for animmersion projection system) and with a rotation at the rim of theaperture β₀ equal to π. The results of the simulation are presented inFIGS. 8A and 8B for a dry projection system and in FIGS. 9A and 9B foran immersion projection system. FIG. 8A shows an intensity profile ofthe projection beam at various focus points around the best focus in theXZ plane and FIG. 8B shows an intensity profile of the projection beamat various focus points around the best focus in the YZ plane.Similarly, FIG. 9A shows an intensity profile of the projection beam atvarious focus points around the best focus in the XZ plane and FIG. 9Bshows an intensity profile of the projection beam at various focuspoints around the best focus in the YZ plane.

From the results, it can be seen that, for a dry projection system, theoverall symmetry of the focus is preserved and in comparison with thedepth of focus obtained using no birefringence (FIGS. 3A and 3B) orusing a linear birefringent polarization modifier (FIGS. 6A and 6B), thedepth of focus obtained using a circular birefringent polarizationmodifier (FIGS. 8A and 8B) has almost doubled. Similarly, for animmersion projection system, it can be seen that the overall symmetry ofthe focus is preserved and in comparison with the depth of focusobtained using no birefringence (FIGS. 4A and 4B) or using a linearbirefringent polarization modifier (FIGS. 7A and 7B), the depth of focusobtained using a circular birefringent polarization modifier (FIGS. 9Aand 9B) has almost doubled.

These results are further seen in FIGS. 10A and 10B which show anintensity contour map in XZ coordinates and YZ coordinates,respectively, for the above discussed configurations, i.e. withoutbirefringence (labeled “clear”), with a linear birefringent polarizationmodifier (labeled “SBR”) and with a circular birefringent polarizationmodifier (labeled “ROT”). The intensity contour map is taken at anormalized intensity value of 0.3 (normalized to the maximum intensity).As can be seen in FIGS. 10A and 10B, the contour that has a largerextension in the Z direction, i.e., a larger depth of focus, correspondsto the situation where a circular birefringent polarization modifier isused.

FIGS. 11A, 11B and 11C show plots of Bossung curves for a dry projectionsystem in the XZ plane, for the above discussed three configurations,i.e. without birefringence, with a linear birefringent polarizationmodifier and with a circular birefringent polarization modifier,respectively. Bossung curves describe a variation of linewidth (andpossibly other parameters) as a function of both focus and exposureenergy. The data is typically plotted as line width versus focus fordifferent exposure energies. From the Bossung curves, it can be seenthat the depth of focus (abscissa in the plots) is larger (from about−400 nm to about 400 nm at the highest exposure intensity) and the CD(ordinate in the plots) is substantially symmetric around the best focusposition (focus position is 0) when using a circular birefringentpolarization modifier (see FIG. 11C). On the other hand, while it can beseen that the depth of focus is broad (from about −300 nm to about 300nm) when using a linear birefringent polarization modifier, the CD is,however, not symmetrical around the best focus position (see FIG. 11B).In this case, it can be noted that the CD is small (about 100 nm for thehighest exposure intensity) for negative values of the focus and larger(about 300 nm for the highest exposure intensity) for positive values ofthe focus (see FIG. 11B). In the case of no birefringence, the CD issubstantially symmetrical around the best focus (with a CD value ofabout 150 nm) but the depth of focus is smaller (extending between about−200 nm and about 200 nm for the highest exposure intensity) (see FIG.11A) compared to the depth of focus obtained when using a circularbirefringent polarization modifier (rotator).

FIGS. 12A, 12B and 12C show plots of Bossung curves for a dry projectionsystem in the YZ plane, for the above discussed three configurations,i.e. without birefringence, with a linear birefringent polarizationmodifier and with a circular birefringent polarization modifier,respectively. Similarly, to the results shown in FIGS. 11A, 11B and 11C,the Bossung curves in FIGS. 12A, 12B and 12C also show the same trendwith the CD being substantially symmetric around the best focus whenusing a circular birefringent polarization modifier and not symmetricaround the best focus when using a linear birefringent polarizationmodifier and with the depth of focus using a circular birefringentpolarization modifier being overall larger than using a linearbirefringent polarization modifier or having in no birefringence.

Generally, there are two approaches for varying circular birefringence.One approach is varying the circular birefringence in the pupil plane ofthe projection system. In this case, a space variant element may be usedto implement the variation of the circular birefringence in the pupilplane. A space variant element is an element where the rotation varieswith the lateral or radial coordinate. Another approach is varying thecircular birefringence in a field plane. In this case, an angularvariant element may be used to implement the variation of the circularbirefringence in the field plane. An angular variant element is anelement where the rotation varies with the angle of propagation. In afield plane, different pupil coordinates are distinguished by theirpropagation angle.

Examples of embodiments for a pupil plane polarization modifier approachinclude using a space variant element, e.g., an optical element such asquartz having a topographical variation or thickness increasing ordecreasing quadratically in height. For example, as shown in FIG. 13,the optical element exhibits a quadratic increase of thickness from acenter of the optical element towards the rim of the optical element.However, as discussed above, in order to use the circular birefringenceof quartz, the crystal axis of the quartz optical element must bealigned parallel to the optical axis and the propagation angles withinthe quartz optical element must be collimated or confined to a fewdegrees. Consequently, this may limit the usable field size.

Another embodiment for a pupil plane approach includes using a rotator,shown in FIG. 14, comprising two half-wave plates WP1 and WP2 where therespective crystal axes A1 and A2 of the two half-wave plates WP1 andWP2 enclose an angle α/2 that increases quadratically to the rim of theaperture.

Examples of embodiments for a field plane approach include usingcrystals with pure circular birefringence or using birefringent coatingssuch as diamond coatings or using right-handed and left-handed chiralthin films.

FIG. 15 shows schematically an embodiment of a lithographic apparatusutilizing a polarization modifier according to an embodiment of thepresent invention. As described previously, lithographic apparatus 10comprises illumination system IL, patterning device (e.g., mask) MA,projection system PL, substrate W and a polarization modifier 20. Thepolarization modifier 20 is shown in this embodiment positioned at theentrance of the projection system, optimally close to the pupil plane,however, one ordinary skill in the art would appreciate that thepolarization modifier 20 can be positioned anywhere in the projectionsystem PL or outside the projection system PL such as, for example,between the patterning device MA and the projection system PL.

Furthermore, since numerous modifications and changes will readily occurto those of skill in the art, it is not desired to limit the inventionto the exact construction and operation described herein. For example,while few materials exhibiting birefringence are discussed herein, itshould be appreciated that other birefringent materials and/orconfigurations are also contemplated. Furthermore, it should beappreciated that the terms pupil plane and field plane as used hereininclude all conjugate planes thereof.

Moreover, the process, method and apparatus of the present invention,like related apparatus and processes used in the lithographic arts, tendto be complex in nature and are often best practiced by empiricallydetermining the appropriate values of the operating parameters or byconducting computer simulations to arrive at a best design for a givenapplication. Accordingly, all suitable modifications and equivalentsshould be considered as falling within the spirit and scope of theinvention.

1. A lithographic apparatus, comprising: a support structure configuredto hold a patterning device, the patterning device configured to patterna beam of radiation; a substrate table configured to hold a substrate; aprojection system configured to project the beam as patterned onto atarget portion of the substrate; and a polarization modifier disposed ina path of the beam, the polarization modifier comprising a materialhaving a radially varying birefringence.
 2. The apparatus according toclaim 1, wherein the birefringence of the material increases radially.3. The apparatus according to claim 2, wherein the variation of therefractive index of the material, An, as a function of pupil coordinatesp and q is given by the equation:${\Delta\quad n} = {\exp\left\{ {i\quad\Delta\quad\varphi_{0}\frac{p^{2} + q^{2}}{{NA}^{2}}} \right\}}$wherein i is the imaginary number, NA is the numerical aperture of theprojection system and Δφ₀ is the value of a retardance at a rim of anaperture of the projection system.
 4. The apparatus according to claim1, wherein the birefringence of the material decreases radially.
 5. Theapparatus according to claim 1, wherein the polarization modifiercomprises a linear polarization modifier.
 6. The apparatus according toclaim 1, wherein the polarization modifier comprises a circularpolarization modifier.
 7. The apparatus according to claim 6, whereinthe circular polarization modifier comprises a rotator having thefollowing Jones matrix: $J = \begin{pmatrix}{\cos\quad\beta} & {{- \sin}\quad\beta} \\{\sin\quad\beta} & {\cos\quad\beta}\end{pmatrix}$ wherein β is a rotation angle.
 8. The apparatus accordingto claim 7, wherein $\beta = {\beta_{0}\frac{p^{2} + q^{2}}{{NA}^{2}}}$where p and q are pupil coordinates, NA is a numerical aperture of theprojection system, and β₀ is an angle of rotation at a rim of anaperture of the projection system.
 9. The apparatus according to claim7, wherein the rotator is a space variant element in which an amount ofrotation of a polarization of the beam varies radially.
 10. Theapparatus according to claim 9, wherein a thickness of the space variantelement increases or decreases radially.
 11. The apparatus according toclaim 10, wherein the space variant element is formed from a materialcomprising quartz.
 12. The apparatus according to claim 7, wherein therotator comprises a first half-wave plate having a first axis and asecond half-wave plate having a second axis, the first axis and thesecond axis enclosing a half angle that increases quadratically to a rimof an aperture of the projection system.
 13. The apparatus according toclaim 7, wherein the rotator comprises an angular variant element inwhich the birefringence varies in a field plane and an amount ofrotation of a polarization of the beam varies with an angle ofpropagation of the beam.
 14. The apparatus according to claim 13,wherein the rotator comprises an optical element having a birefringentcoating deposited thereon.
 15. The apparatus according to claim 13,wherein the rotator comprises an optical element formed of right-handedand left-handed chiral thin films.
 16. The apparatus according to claim1, wherein the polarization modifier increases a depth of focus of alithographic process implemented by the apparatus.
 17. The apparatusaccording to claim 1, wherein the depth of focus is approximatelydoubled in size compared to a depth of focus obtained in a lithographicprocess performed with a lithographic apparatus without the polarizationmodifier.
 18. The apparatus according to claim 1, wherein a criticaldimension of a printed feature on the substrate is substantiallysymmetrical around a best focus position.
 19. The apparatus according toclaim 1, wherein the polarization modifier is disposed in a pupil planeof the projection system or in a vicinity of the pupil plane.
 20. Theapparatus according to claim 1, wherein the polarization modifier isdisposed between the patterning device and the projection system.
 21. Alithographic apparatus, comprising: a support structure configured tohold a patterning device, the patterning device configured to pattern abeam of radiation; a substrate table configured to hold a substrate; aprojection system configured to project the beam as patterned onto atarget portion of the substrate; and a polarization modifier disposed ina path of the beam, the polarization modifier comprising a materialhaving a radially continuously varying birefringence.
 22. The methodaccording to claim 21, wherein the birefringence of the materialincreases or decreases radially.
 23. The apparatus according to claim21, wherein the polarization modifier is a space variant element inwhich an amount of rotation of a polarization of the beam variesradially.
 24. The apparatus according to claim 23, wherein a thicknessof the space variant element increases or decreases radially.
 25. Theapparatus according to claim 21, wherein the polarization modifiercomprises a first half-wave plate having a first axis and a secondhalf-wave plate having a second axis, the first axis and the second axisenclosing a half angle that increases quadratically to a rim of anaperture of the projection system.
 26. The apparatus according to claim21, wherein the polarization modifier comprises an angular variantelement in which the birefringence varies in a field plane and an amountof rotation of a polarization of the beam varies with an angle ofpropagation of the beam.
 27. A method for manufacturing a device,comprising: projecting a patterned beam of radiation through apolarization modifier comprising a material having a radially varyingbirefringence onto a target portion of a substrate.
 28. The methodaccording to claim 27, wherein the birefringence of the materialincreases or decreases radially.
 29. The method according to claim 27,wherein the birefringence of the material varies substantiallycontinuously.
 30. The method according to claim 27, wherein thepolarization modifier comprises a linear polarization modifier.
 31. Themethod according to claim 27, wherein the polarization modifiercomprises a circular polarization modifier.
 32. The method according toclaim 31, wherein the circular polarization modifier comprises a spacevariant element in which an amount of rotation of a polarization of thepatterned beam varies radially.
 33. The method according to claim 31,wherein the circular polarization modifier comprises a first half-waveplate having a first axis and a second half-wave plate having a secondaxis, the first axis and the second axis enclosing a half angle thatincreases quadratically to a rim of an aperture of a projection systemused to project the patterned beam.
 34. The method according to claim31, wherein the circular polarization modifier comprises an angularvariant element in which birefringence varies in a field plane and anamount of rotation of a polarization of the patterned beam varies withan angle of propagation of the patterned beam.
 35. The method accordingto claim 27, wherein projecting the patterned beam through thepolarization modifier increases a depth of focus.
 36. The methodaccording to claim 27, further comprising printing a feature on thesubstrate, wherein a critical dimension of the printed feature issubstantially symmetrical around a best focus position.